14\ntype the correct answer in each box. use ...
14\ntype the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s).\nthe mean score on a biology exam taken by all undergraduate students in a college in a particular year is 67.8 with a standard deviation of 11.5\nthe standard error of the mean for a sample of 70 students is , and the margin of error of the mean is (round off your answers to the nearest hundredth.)
Answer
# Answer:
Standard error of the mean: 1.37, Margin of error of the mean: 2.69
# Explanation:
## Step1: Recall standard - error formula
The formula for the standard error of the mean ($SE$) is $SE=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size. Given $\sigma = 11.5$ and $n = 70$.
$SE=\frac{11.5}{\sqrt{70}}\approx\frac{11.5}{8.37}\approx1.37$
## Step2: Recall margin - of - error formula
For a 95% confidence interval (common in statistics when no confidence level is specified), the margin of error ($ME$) for the mean is $ME = z\times SE$, where the $z$ - score for a 95% confidence interval is approximately $z = 1.96$.
$ME=1.96\times1.37\approx2.69$